Department of Economics
University of Maryland
Economics 325
Intermediate Macroeconomic Analysis
Practice Problem Set 4
Professor Sanjay Chugh
Spring 2011
1.
Optimal Choice in the ConsumptionSavings Model with Credit Constraints:
A
Numerical Analysis.
Consider our usual twoperiod consumptionsavings model.
Let preferences of the representative consumer be described by the utility function
12
1
2
(, )
,
uc c
c
c
E
±
where
1
c
denotes consumption in period one and
2
c
denotes consumption in period
two.
The parameter
is known as the subjective discount factor and measures the
consumer's degree of impatience in the sense that the smaller is
, the higher the
weight the consumer assigns to present consumption relative to future consumption.
Assume that
1/1.1.
For this particular utility specification, the marginal utility
functions are given by
112
1
1
2
ucc
c
and
212
2
2
c
.
The representative household has initial
real
financial wealth (including interest) of
0
(1
)
1
ra
±
.
The household earns
1
5
y
units of goods in period one and
2
10
y
units in period two.
The real interest rate paid on assets held from period one to
period two equals 10% (i.e.,
0.1
r
).
a.
Calculate the equilibrium levels of consumption in periods one and two (
Hint:
Set up the Lagrangian and solve.)
b.
Suppose now that lenders to this consumer impose
credit constraints
on the
consumer.
Specifically, they impose the tightest possible credit constraint – the
consumer is not allowed to be in debt at the end of period one, which implies that
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 Spring '08
 chugh
 Economics, Utility, Period, representative, credit constraint

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